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It is known that when a Random Access Machine halts the output on the registers is going to be $R_1,\ldots,R_{||R_0||}$ after going through its instruction set where $||R_0||$ denotes the length of the binary representation of $R_0$. Is there any implication changing the output on the registers as $R_1,\ldots,R_{R_0}$.

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  • $\begingroup$ No, not really, though the exact answer depends on the instruction set. It's mostly a matter of convention, since you can convert between the two possibilities pretty quickly. $\endgroup$ – Yuval Filmus Mar 1 '16 at 18:39

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